For Array Exponentiation.
B=A^2
B=A*A
C=A^3
C=A*A*A
For array multiplication, to be valid i.e.
A*A
the following condition must be met
<span style="color: #ffcc00;">n1</span>=<span style="color: #00ccff;">m2</span>
. Now for array exponentiation, the two arrays being multiplied are the same thus
<span style="color: #ffcc00;">n1</span>=<span style="color: #00ccff;">m1</span>
and
<span style="color: #ffcc00;">n2</span>=<span style="color: #00ccff;">m2</span>
and because
<span style="color: #ffcc00;">n1</span>=<span style="color: #00ccff;">m2</span>
the only condition which satisfies the rule of matrix multiplication is that of a square matrix i.e.
<span style="color: #ffcc00;"><span style="color: #00ccff;">m1</span></span>=<span style="color: #00ccff;">m2</span>
.
A=[1,2;3,4]
B=[1,2;3,4]^2
B=[1,2;3,4]*[1,2;3,4]
C=[1,2;3,4]^3
C=[1,2;3,4]*[1,2;3,4]*[1,2;3,4]
B=[1,2;3,4]^2
B=[1,2;3,4]*[1,2;3,4]
C=[1,2;3,4]^3
C=[1,2;3,4]*[1,2;3,4]*[1,2;3,4]
